Simplify the following expression: $r = \dfrac{18k^3 - 18k^2}{-78k^2}$ You can assume $k \neq 0$.
Solution: Find the greatest common factor of the numerator and denominator. The numerator can be factored: $18k^3 - 18k^2 = (2\cdot3\cdot3 \cdot k \cdot k \cdot k) - (2\cdot3\cdot3 \cdot k \cdot k)$ The denominator can be factored: $-78k^2 = - (2\cdot3\cdot13 \cdot k \cdot k)$ The greatest common factor of all the terms is $6k^2$ Factoring out $6k^2$ gives us: $r = \dfrac{(6k^2)(3k - 3)}{(6k^2)(-13)}$ Dividing both the numerator and denominator by $6k^2$ gives: $r = \dfrac{3k - 3}{-13}$